1)
Let \(B\)  be a left cancellative left semi-brace of size \(pq\)  (where \(p,q\)  are prime numbers with \(p>q\) ) and with \(|E|>1\) . Then, if \(|E|=p\)  or if \((B,\circ )\)  is abelian, \(B\)  is right nilpotent by [1]}. If \(|E|=q\)  and \((B,\circ )\)  is not abelian, then \(B\)  is isomorphic to the semidirect product of left semi-braces \(G\rtimes _{\alpha } E\) , therefore by rnilp1 and rnilp2 \(B\)  is a right nil left semi-brace which is not right nilpotent.
2)
Let \(B\)  be a left cancellative left semi-brace of size \(2p^2\) . If \(|E|=p^2\)  or if \((B,\circ )\)  is abelian, by [1]} it is right nilpotent. While, if \(|E|=2\) , \((B,\circ )\)  is not abelian and \(G\)  is a trivial skew left brace of size \(p^2\) , by rnilp1 and rnilp2 \(B\)  is a left cancellative left semi-brace right nil but not right nilpotent.


